Semiclassical initial-value-representation study of helium scattering from Cu(110)

The final momentum distribution for the scattering of He from a corrugated surface representation of Cu(110) is obtained from semiclassical theory. We derive a formally exact expression for the distribution which involves the absolute value squared of a single overlap of the initial wave function with the final momentum state. This reduces the number of phase-space integrals appearing in the semiclassical expressions and therefore leads to a large reduction in the computational effort. In addition, other energy-dependent observables are directly accessible from the momentum distribution without the need for further simulations. Using this formalism, we compare the quality of results obtained using a classical Wigner approximation and the frozen Gaussian, Herman-Kluk, and thawed Gaussian semiclassical propagators. We find that the thawed Gaussian is not only the best approximation, but it also converges more rapidly than the other semiclassical methods. The frozen Gaussian Herman-Kluk propagator is superior to the frozen Gaussian propagator. In contrast, the classical Wigner approach is qualitatively wrong as it does not properly account for the interference which dominates the angular distribution.